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Latent Tree Models &
Statistical Foundation for TCM
Nevin L. Zhang
Joint Work with: Chen Tao, Wang Yi, Yuan Shihong
Department of Computer Science & Engineering
The Hong Kong University of Science & Technology
http://www.cse.ust.hk/~lzhang/
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Learning Latent Tree Models & TCM
Publications
N. L. Zhang, S. H. Yuan, T. Chen and Y. Wang (2008). Latent tree models
and diagnosis in traditional Chinese medicine. Artificial Intelligence in
Medicine. 42, 229-245.
N. L. Zhang, S. H. Yuan, T. Chen and Y. Wang (2008). Statistical
Validation of TCM Theories. Journal of Alternative and Complementary
Medicine. Accepted.
N. L. Zhang, S. H. Yuan, T. Chen, and Y. Wang (2007). Hierarchical Latent
Class Models and Statistical Foundation for Traditional Chinese
Medicine 11th Conference on Artificial Intelligence in Medicine (AIME
07), 07-11, July 2007, Amsterdam, The Netherlands.
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Learning Latent Tree Models & TCM
Latent Tree Models (LTM)
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Bayesian networks with
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Rooted tree structure
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Discrete random variables
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Leaves observed (manifest variables)
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Internal nodes latent (latent variables)
Also known as hierarchical latent class
(HLC) models, HLC models
P(Y1),
P(Y2|Y1),
P(X1|Y2), P(X2|Y2), …
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Learning Latent Tree Models & TCM
Example
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Manifest variables
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Math Grade, Science Grade, Literature Grade, History Grade
Latent variables
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Analytic Skill, Literal Skill, Intelligence
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Learning Latent Tree Models & TCM
Learning Latent Tree Models: The problem
X1
X2
…
X6
X7
1
0
…
1
1
1
1
…
0
0
0
1
…
0
1
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Determine
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Number of latent variables
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Cardinality of each latent variable
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Model Structure
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Conditional probability distributions
Learning Latent Tree Models & TCM
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Learning Latent Tree Models: The Algorithms
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Model Selection
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Several scores examined: BIC, BICe, CS, AIC, holdout likelihood
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BIC: best choice for the time being
Model optimization
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Double hill climbing (DHC), 2002
 7 manifest variables.
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Single hill climbing (SHC), 2004
 12 manifest variables
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Heuristic SHC (HSHC), 2004
 50 manifest variables
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EAST, 2008
 As efficient as HSHC, and finds better models
Learning Latent Tree Models & TCM
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Traditional Chinese Medicine (TCM)
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TCM statement:
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Yang deficiency (阳虚): intolerance to cold (畏寒), cold limbs (肢冷), cold
lumbus and back (腰背冷), and so on ….
Regarded by many as not scientific, even groundless.
Two aspects to the meaning
1.
Claim: There exists a class of patients, who characteristically have the cold
symptoms . The cold symptoms co-occur in a group of people,
2.
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Explanation offered: Due to deficiency of Yang. It fails to warm the body
What to do?
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Previous work focused on 2.
New idea: Do data analysis for 1
Learning Latent Tree Models & TCM
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Objectivity of the Claimed Pattern
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TCM Claim: there exits a class of patients, in whom symptoms such
as ‘intolerance to cold’, ‘cold limbs’, ‘cold lumbus and back’, and so on
co-occur at the same time
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How to prove or disapprove that such claimed TCM classes exist in the
world?
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Systematically collect data about symptoms of patients.
 Perform cluster analysis, obtain natural clusters of patients
 If the natural clusters corresponds to the TCM classes, then YES.
1. Existence of TCM classes validated
2. Descriptions of TCM classes refined and systematically expanded
3. Establish a statistical foundation for TCM
Learning Latent Tree Models & TCM
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Why Latent Tree Models?
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TCM uses multiple interrelated latent concepts to explain co-occurrence
of symptoms
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Yang deficiency (肾阳虚) , Yin deficiency (肾阴虚): , Essence insufficiency (肾
精亏虚) , …
TCM theories are latent structure models in natural language.
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Need latent structure models
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With multiple interrelated latent variables..
Latent Tree Models are the simplest such models
Learning Latent Tree Models & TCM
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Empirical Results
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Can we find the claimed TCM classes using latent tree models?
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We collected a data set about kidney deficiency (肾虚)
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35 symptom variables, 2600 records
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Learning Latent Tree Models & TCM
Result of Data Analysis
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Y0-Y34: manifest variables from data
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X0-X13: latent variables introduced by data analysis
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Structure interesting, supports TCM’s theories about various symptoms.
(Zhang et al. 2008, AI in Medicine)
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Learning Latent Tree Models & TCM
Latent Clusters
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X1:
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5 states: s0, s1, s2, s3, s4
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Samples grouped into 5 clusters
Cluster X1=s4
{sample | P(X1=s4|sample) > 0.95} 
Cold symptoms co-occur in samples
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Class implicitly claimed by TCM found!
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Description of class refined
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By Math vs by words
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Learning Latent Tree Models & TCM
Statistical Validation of TCM Theory
LT
Model
TCM
Theory
Ancient Times
2000-2008
Experiences
Data
Learning Latent Tree Models & TCM
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Other TCM Data Sets
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From Beijing U of TCM, 973 project
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Depression
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Hepatitis B
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Chronic Renal Failure
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…
China Academy of TCM
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Subhealth
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Type 2 Diabetes
In all cases, claimed TCM classes
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Validated
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Quantified and refined
Learning Latent Tree Models & TCM
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Another Perspective
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Just now: validation of TCM theory.
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Another perspective: improve diagnosis
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TCM diagnosis: classification
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Problems: boundaries between classes not clear
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Our work is helpful in clarifying the boundaries
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Learning Latent Tree Models & TCM
Conclusions
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Latent tree models, and latent structure models in general, offer
framework for
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Density estimation
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Latent structure discovery
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Multidimensional clustering.
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Can play a fundamental role in modernizing TCM
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Can be useful in many other areas
 Probabilistic inference, classification, semi-supervised learning…
 marketing, survey studies, ….
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We have only scratched the surface.
Thank You!